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In the former part of this paper, we give functional equations for Barnesmultiple zeta-functions and consider some relevant results. In particular, weshow that Ramanujan's classical formula for the Riemann zeta values can bederived from functional equations for Barnes zeta-functions. In the latter halfpart, we generalize some evaluation formulas of certain series involvinghyperbolic functions in terms of Bernoulli polynomials. The original formulaswere classically given by Cauchy, Mellin, Ramanujan, and later recovered andformulated by Berndt. From our consideration, we give multiple versions ofthese known formulas.

Barnes multiple zeta-functions, Ramanujan's formula, and relevant series involving hyperbolic functions